Sorry, I forgot to put the last paragraph as a quote.
https://en.m.wikipedia.org/wiki/Eth#Old_English
~~https://www.youtube.com/watch?v=IwvbNppHZkg~~
Dang, the creator put a paywall on it.
It's the same with the letter f, from what I remember it was pronounced as an f or a v, depending on what letters are before and after it, similar to lenition in Irish, or s being pronounced as both s and z in Romance languages depending on what's around it.
Here we go
https://oldenglish.info/advpronunciationguide.html
Specifically þ and ð:
þ and ð are digraphs. This means they represent the same sound, much like the modern 'th' can be voiced (in words like 'this' and 'that') or unvoiced (in words like 'thick' or 'through'). The general rule of thumb is that þ comes at the start of a word and ð comes in the middle or at the end. However, you will often see them used interchangeably, with the same word appearing on the same page spelled with both ð forms and þ forms. You can even see words like 'oþþe' spelled 'oþðe' or 'oððe' so don't overthink it.
See my post to the reply above yours :)